Two masses of $8\,kg$ and $4\,kg$ are connected by a string as shown in the figure over a frictionless pulley. The acceleration of the system is ............ $m/s^2$.

The horizontal acceleration that should be given to a smooth inclined plane of angle $\sin^{-1} (1/l)$ to keep an object stationary on the plane relative to the inclined plane is

Two masses $M_1$ and $M_2$ are attached to the ends of a string which passes over a pulley attached to the top of a double inclined plane of angles of inclination $\alpha$ and $\beta$. If the system is released,the acceleration $a$ of the system is given by:

$A$ body of mass $5\,kg$ is suspended by a spring balance on an inclined plane as shown in the figure. The spring balance measures ............ $N$.

$A$ solid sphere,a hollow sphere,and a ring are released from the top of a frictionless inclined plane,causing them to slide down the plane. For which object is the acceleration down the plane the maximum?

Block $A$ of weight $100 \, N$ rests on a frictionless inclined plane of slope angle $30^{\circ}$. $A$ flexible cord attached to $A$ passes over a frictionless pulley and is connected to block $B$ of weight $w$. Find the weight $w$ for which the system is in equilibrium.